1. Have you checked the charger? Make sure the contacts on the side that slides into the DS aren't bent or broken. If this is an issue just replace the charger. 2. You may also need to replace the battery if the battery is not holding a charge. And if those two things do not solve the issue: 3. It's fairly common over a period of time for the charging port inside the DS to become worn out. Get a flashlight and take a look at the charging port to see if anything looks bent or broken. If this is the issue you would need to bring it to one of those cell phone repair shops (I would call beforehand to make sure they work on handheld gaming systems) otherwise you might have to buy all the soldering equipment and parts and do the soldering job yourself. Good Luck!
Make sure your software is updated for your OS and if you use any apps that have access to texting make sure they are updated or uninstalled if you don't need them. Sounds like a software issue.
If you are using one of those ISP hotspots that require prepaid access or an account you would log in with your username and password for your ISP account after adding the wifi connection in your settings. A browser should popup asking your login credentials. Otherwise, if you are trying to connect to an open network just choose the network in your wifi settings.
1. When you go to settings and try to pull up wifi list does it show any connections at all? (yours, neighbors, etc.) - If no connections are shown make sure airplane mode is off and your wifi setting is turned on, otherwise you have a wireless card failure. -If you do see connections and attempt to connect to your network is it giving you an error? If its a password error and you know the password is right, forget the network (normally by holding down on the highlighted network and select forget) and add it again and try. If it is another error please post. -If you do see other's connections and not your own then make sure your 2.4 ghz bandwidth frequency is turned on, some devices do not have the hardware to see the 5ghz frequency.
As with the above post I would also check if it is connected to a power strip if the strip is functioning properly. Those do go out from time to time. Try an outlet you know that works.
I have had to call Pop-A-Lock before because I have done just this before. I hope you have your phone on you and not in the car but try to contact a company like Pop-A-Lock.
Cell phones don't have internal fans like a computer and rely heavily on design for airflow and cooling. Apple is really uptight about having your phone fixed at a non-apple tech and doesn't make its replacement parts that readily available; you can find "compatible" parts but using those or the non-apple tech technically voids any warranty on the device. So, although the guys in the mall mean well and are probably doing a good job, they are also most likely not using apple replacement parts and the parts they do use could interfere with the airflow of the original design. Aside from that, did you get a new case after the screen fix? Some cases smother phones more than others, obstructing airflow.